Details

Time bar (total: 4.9s)

sample346.0ms

Algorithm
intervals
Results
7.0ms40×body2560valid
6.0ms196×body80valid
4.0ms20×body1280valid
3.0ms94×body80nan
1.0ms14×body640valid
1.0ms7×body320valid
0.0ms4×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (* b_2 b_2) (* a c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
71.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms
(- (* b_2 b_2) (* a c))
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05493055
118262150
250022063

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b
(- (* b_2 b_2) (* a c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
63×*-un-lft-identity
61×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-exp-log associate-*r*
11×times-frac fma-neg
10×add-log-exp
9×add-cbrt-cube
7×pow1 neg-mul-1 associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg sqrt-div div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 169
Calls
4 calls:
86.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms
(- (* b_2 b_2) (* a c))
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
34.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06092985
123341993
250021940

prune291.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b
(- (* b_2 b_2) (* a c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
165×times-frac
118×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
15×add-exp-log
11×fma-neg
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×neg-mul-1 flip3-- div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 257
Calls
4 calls:
44.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
10.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
34.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07704550
132153424
250023236

prune339.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (* b_2 b_2) (* a c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
70.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05493056
118142150
250012063

prune281.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.2b

regimes260.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.2b

bsearch69.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
7.895438119410103e+91
7
-1.9209620939201072e-35
-4.595080940101684e-37
-3.429521559957367e-36

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03817
14417
24417

end0.0ms

sample1.0s

Algorithm
intervals
Results
190.0ms1043×body2560valid
171.0ms5856×body80valid
126.0ms915×body1280valid
88.0ms2942×body80nan
51.0ms475×body640valid
23.0ms257×body320valid
20.0ms97×body5120valid
5.0ms96×body160valid